Foreign Exchange Intervention Redux

Roberto Chang∗

Rutgers University and NBER

This Version: November 2017†

Abstract

Received wisdom posits that sterilized foreign exchange intervention can be effective

by altering the currency composition of assets held by the public. This paper proposes an

alternative channel: sterilization may (or may not) have real effects because it changes the

net credit position of the central bank vis a vis financial intermediaries, thereby affecting

external debt limits. This argument is developed in the context of an open economy

model with a financial intermediation sector subject to occasionally binding collateral

constraints. FX intervention has real effects if and only if it occurs when the constraints

bind; at such times, a sterilized sale of offi cial reserves relaxes the constraints by reducing

the central bank’s debt to domestic banks, freeing resources for the latter to increase

the supply of credit to domestic agents. Several novel implications for the analysis of

FX intervention policy, offi cial reserves accumulation, and the interaction between FX

intervention and monetary policy are derived.

∗Email: chang@econ.rutgers.edu†Preliminary Draft. Prepared for the 2017 Central Bank of Chile Annual Conference. I am thankful to Luis

Felipe Céspedes and seminar participants at Rutgers, ITAM, and Banco de Mexico for useful comments andsuggestions. Of course, any errors or shortcomings are solely mine.

1

1 Introduction

Arguably, no issue in International Macroeconomics exhibits more dissonance between academic

research and policy practice than foreign exchange intervention. The dominant view from

academia is that sterilized foreign exchange (FX) intervention has a tiny, if any, impact on

real variables, which makes it virtually useless as an independent macroeconomic policy tool.

Indeed, a large body of empirical literature has struggled to find a consistent link between

FX intervention and macroeconomic aggregates, including exchange rates.1 From a theory

perspective, this is hardly surprising, especially since modern dynamic macroeconomic models

often predict that FX intervention should be irrelevant (Backus and Kehoe 1989).

Policymakers, on the other hand, have ignored the prescriptions from research and have

intervened, frequently and intensely, in the foreign exchange market. In advanced countries,

such as Switzerland, FX intervention has become prominent and noticeable following the global

financial crisis, while in emerging economies FX intervention was the norm already before the

crisis, and even in countries committed to inflation targeting. Interestingly, central bankers

reportedly believe that FX intervention is effective as a policy tool, and that it has been used

successfully.2

The purpose of this paper is to develop a recent perspective on FX intervention which,

among other advantages, can help reconciling the contrasting views of academics and policy

makers. Following Céspedes, Chang, and Velasco (2017), I adopt the view that FX intervention

can and should be seen as a specific instance of the so called "unconventional" central bank

policies reviewed, for example, in Gertler and Kiyotaki (2010). This view strongly indicates

that a useful analysis of FX intervention requires a framework that allows for financial frictions

and institutions, for otherwise unconventional policies turn out to be irrelevant (as in Wallace

1981 or, as already mentioned, Backus and Kehoe 1989).

1For instance, citing Obstfeld (1982) and Sarno and Taylor (2001), Taylor (2014, p. 369) writes: "theevidence is often weak and a source of ongoing controversy". A more recent survey of the empirical literatureis Menhoff (2013).

2See Chutasripanish and Yetman (2015). Also, Adler and Tovar (2011).

2

Accordingly, I analyze FX intervention in an extension of Chang and Velasco’s (2017) model

of a small open economy. In that economy, financial intermediaries or banks borrow from the

world market and, in turn, extend credit to domestic households or the government, subject

to an external debt limit. The model is standard and intended to be as simple as possible to

help exposition, so as to isolate two features that turn out to be central. The first one is the

specification of sterilized intervention. Sterilized FX interventions are operations in which the

central bank buys (or sells) offi cial reserves of foreign exchange, and at the same time it sells

(or buys) an offsetting amount of securities, such as "sterilization bonds". This implies that

the central bank issues sterilization bonds, or more generally reduces its net credit position,

when it purchases reserves, and it cancels the bonds when it sells reserves.

The second aspect of our model is that domestic banks face an external debt limit that may

or may not bind in equilibrium. This is key because, as I show, FX intervention has no impact

on macroeconomic aggregates if it occurs at times at which that constraint limit does not bind.

Conversely, as I also show, FX intervention does affect equilibrium real outcomes at times of

binding financial constraints.

More precisely, sterilized FX intervention can affect equilibrium because the associated

sterilization operations relax or tighten financial constraints. When the central bank sells

foreign exchange, in particular, sterilization means that the central bank cancels sterilization

bonds (or, more generally, increases its net credit position vis a vis domestic banks). If financial

constraints do not bind, domestic banks accommodate this change by simply borrowing less

from the world market, and equilibrium is left undisrupted. But when financial constraints do

bind, the fall in the central bank’s demand for credit implied by sterilization frees resources for

banks, allowing them to increase the supply of loans to the domestic private sector. The result

is that loan interest rates fall, and aggregate demand expands.

This view of the mechanism through which sterilized FX intervention works differs sharply

from alternative ones, and in particular from those of currently dominant portfolio balance

models. Such models assume that domestic currency bonds and foreign currency bonds are

3

imperfect substitutes and, as a result, uncovered interest parity holds up to a risk premium

that depends on the ratio of domestic currency bonds to foreign currency bonds in the hands of

the public. Sterilized FX intervention affects that ratio and hence, the UIP risk premium, which

in turn requires macroeconomic adjustments. In contrast, the mechanism proposed in this paper

does not rely on imperfect asset substitutability nor on differences in currency denomination;

in fact, I show that FX intervention can be an effective policy tool (when financial constraints

bind) under perfect asset subtitutability and even if the economy is "financially dollarized".

As a significant additional payoff, our exploration of the model highlights a close link between

sterilized intervention and the cost-benefit analysis of offi cial reserves accumulation. Under the

natural assumption that the central bank cannot issue foreign currency, maintaining a large

stock of foreign exchange enhances the ability of the central bank to stimulate the economy,

by selling reserves, when financial constraints become binding. This is obviously beneficial and

intuitive. But in this model there is also a cost of holding reserves, namely, that larger reserves

also imply larger outstanding quantities of sterilization bonds, the financing of which put banks

closer to their credit limits, making them more vulnerable to adverse exogenous shocks. In

other words, the main tradeoff is that large amounts of offi cial reserves allow the central bank

to respond more effectively, via FX intervention, when financial constraints are hit, at the cost

of those constraints being hit more frequently.

We use the model to derive several lessons for FX intervention rules and their relation

to conventional monetary policy. Notably, we find that a policy of selling reserves when the

exchange rate is weak and buying reserves when it is strong can relax financial constraints

when they bind, but also that there is intervention when the constraints do not bind, which

can be counterproductive. A policy of intervention based on credit spreads is superior, as it

is only activated when financial constraints bind. Also, the question of whether sterilized FX

intervention can be an independent policy tool that can complement conventional monetary

policy has an affi rmative answer in our model. But the fact that financial constraints bind only

occasionally is crucial and means, in particular, that one must go beyond the analysis of linear

4

models or linear approximations around the steady state.

Finally, our approach yields several other appealing insights. Specifically, it is consistent

with the empirical diffi culty to find significant macroeconomic effects of FX intervention in

the data, for our model implies that intervention matters only at times of binding constraints,

which may be infrequent. It also indicates how FX intervention can be welfare improving. And

it sheds light on the role of the so called quasi fiscal deficits that central banks derive from FX

intervention.

This paper is a contribution to a large literature on FX intervention. For useful surveys,

see Sarno and Taylor (2001), Menkoff (2013), Adler and Tovar (2011), and Ostry, Ghosh,

and Chamon (2016). Until the powerful critique by Backus and Kehoe (1989), the literature

was dominated by models derived from the optimal portfolio choices of investors that viewed

domestic currency assets and foreign currency assets as imperfect substitutes. Recently the

portfolio balance approach has experienced a revival, led by Benes, Berg, Portillo, and Vavra

(2015), and followed by Vargas, González and Rodriguez (2013), Montoro and Ortiz (2016),

and Cavallino (2017).

The newer portfolio balance models are similar to ours in that FX intervention can have

real effects because of the interaction of sterilization operations with financial frictions. They

differ substantially along some important details, however. For example, Benes et al. (2015)

and Vargas et al. (2013) impose that banks pay portfolio management costs similar to those

in Edwards and Vegh (1997). They make assumptions about those costs that make domestic

currency bonds and foreign currency bonds imperfect substitutes for the banks, which leads to

the same kind of uncovered interest parity condition cum risk premium that was the hallmark

of the older portfolio balance approach. This indicates that, while the newer models have been

successful in providing satisfactory theoretical underpinnings to the portfolio balance approach,

they still have to be reconciled with the same evidence as older models. In comparison, in the

model of this paper, financial frictions only bite sometimes and not others, which makes a

significant difference in the results. For one thing, under the assumption that financial con-

5

straints are not binding in the steady state, our model implies that FX intervention is irrelevant

for shocks that are not large enough to drive the economy to the financially constrained re-

gion. This is consistent with the scarcity of empirical evidence of nontrivial effects of sterilized

intervention on macro variables.

Section 2 of this paper presents the model that serves as the basis for our discussion. A

baseline version of the model assumes complete price flexibility and financial dollarization. In

that baseline version, Section 3 discusses FX intervention and reserves accumulation. Nominal

price rigidities and, hence, a nontrivial role for monetary policy are introduced in Section 4.

That section examines the interaction between monetary policy and FX intervention. Section

5 shows how the assumption of financial dollarization can be relaxed, with only minor changes

in our arguments. Section 6 concludes.

2 A Model of FX Intervention and Reserves Accumula-

tion

This section develops a basic open economy model that will serve to express our ideas regarding

intervention policy. I extend the model of Chang and Velasco (2017) to an stochastic setting

and, more importantly, to examine in detail the mechanism of sterilized intervention, and how

FX intervention policy interacts with financial constraints that bind only occasionally.

In order to focus on the essentials, this section imposes very restrictive assumptions. In

particular, it assumes perfectly flexible prices (so that conventional monetary policy has no

bite) and that all financial assets are denominated in foreign currency (complete financial dol-

larization). These assumptions not only simplify the analysis but also serve to emphasize that

the mechanism by which FX intervention works does not depend on the currency denomina-

tion of assets, or the interaction with other monetary policy tools. Of course, realistic models

will require adding nominal price rigidities, powerful monetary policy, and differences in the

currency denomination of assets. But these can be added at relatively little extra cost later, as

6

shown in sections 4 and 5.

2.1 Commodities and Production

We consider an infinitely lived, small open economy. In each period there are two internationally

traded goods, home and foreign. The price of the foreign good in terms of a world currency

(called "dollar") is fixed at one.

The home good is the usual Dixit-Stiglitz aggregate of varieties, with elasticity of substi-

tution ε. There is a continuum of monopolistically competitive firms indexed by i in [0, 1]. In

period t, firm i produces variety i via yit = Anit, where nit denotes labor input and A a pro-

ductivity term, assumed to be constant for ease of exposition. Firms take wages as given, so

that nominal marginal cost in period t is common to all, and given by:

MCt = Wt/A (1)

where Wt is the nominal wage, that is, the wage expressed in terms of a domestic currency

("peso" hereon).

For now, we assume flexible prices, meaning that, in every period, all firms set a peso price

for their produce. All varieties then carry the same price in equilibrium, given by the usual

markup rule:

Pht =

(1− 1

ε

)MCt (2)

Pht is also the price of the domestic home aggregate good. That aggregate is sold at home

and abroad. The foreign part of demand is given simply by a function xeχt of its relative price,

the real exchange rate:

et ≡EtPht

with Et denoting the nominal exchange rate (pesos per dollar), and x and χ positive parameters.

Home demand for the domestic aggregate good is related to the demand for final consump-

7

tion, which is denoted by ct and assumed to be a Cobb Douglas function of the domestic

composite good and foreign goods. The Law of One Price is assumed to hold,implying that the

peso price of foreign goods is given by Et. Then the price of final consumption (the CPI) is

Pt = Pαh,tE

1−αt

where α is a parameter between zero and one.

The implied demand for the home aggregate is cht = αe1−αt ct, and therefore the market

clearing condition for home output is

yt = αe(1−α)t ct + xeχt , (3)

2.2 Banks

There is a large number of domestic financial intermediaries or banks, which borrow from the

rest of the world to lend to either households or the government, subject to financial frictions.

A representative bank starts a period t with an amount of capital or net worth of kt dollars.

This amount is, as we will see, raised from domestic households in exchange for a share of the

bank’s next period profits. Given kt, the bank borrows dt dollars from foreigners, at a gross

interest rate of R∗t ≥ 0, which the bank takes as given.

Because of financial frictions, external borrowing is restricted by a collateral constraint

dt ≤ θkt

where θ is a constant. As noted in the literature, this kind of constraint can be rationalized in

various ways. 3

The resources raised by the bank can be devoted to issue domestic loans to the private

3For example, one may assume that, after raising dt, the banker can "abscond" with the funds at a cost ofθ times equity. Knowing this, lenders will not extend more credit than θkt .

8

sector, lt , or to purchase bonds issued from the central bank, bt. For the time being, we assume

that private loans and central bank bonds are perfect substitutes and carry the same interest

rate, %t, between periods t and t+ 1.

Observe that we assume, for now, that loans and bonds, and the interest rate, are all

denominated in dollars. This case, sometimes termed "financial dollarization", may be realistic

for some countries and not for others. However, it is the simplest assumption to start with.

More importantly, it emphasizes that the basic mechanism by which FX intervention works in

our setting does not rely on differences in currency denomination. With that mechanism laid

out, section 5 turns to its interaction with peso denominated loans and bonds.

Then, the bank’s balance sheet requires that:

bt + lt = kt + dt.

and the bank’s profits are given by

πt+1 = (1 + %t)(lt + bt)−R∗tdt,

Note that, under our maintained assumptions, profits are realized in period t + 1 but they

are known as of period t. The bank’s problem, therefore, is simply to choose bt, dt, and lt to

maximize πt+1 subject to the collateral constraint.

The solution is simple. Combining the preceding two equations, profits can be written as

πt+1 = R∗tkt + (1 + %t −R∗t )(lt + bt)

i.e. profits are a sum of a "normal " return on equity plus an excess return on domestic credit.

Hence, if 1 + %t = R∗t , there are no supranormal returns, and the bank’s optimal policy is

indeterminate as long as bt + lt = kt + dt and dt ≤ θkt. If 1 + %t > R∗t , on the other hand,

the bank lends as much as it can. The collateral constraint then binds, so that dt = θkt, and

9

bt + lt = (1 + θ)kt.

Finally, the return to equity is denoted by (1 + ωt)R∗t ≡ πt+1/kt, and given by:

πt+1

kt= R∗t + (1 + %t −R∗t )(1 + θ) ≡ (1 + ωt)R

∗t

2.3 Central Bank, Intervention, and Reserves Accumulation

The essence of sterilized FX intervention is that a central bank sells or buys foreign exchange

and, at the same time, buys or sells a matching amount of securities. This can be implemented

in a myriad ways, and the menu of alternatives depends in practice on institutional aspects

of each economy, such as the kind of securities that are involved in sterilization. But, and as

emphasized in the literature, the crucial aspect of sterilized intervention is that it involves a

simultaneous change in offi cial reserves and the net credit position of the central bank.

Accordingly, in what follows we assume that sterilized FX intervention means that the

central bank buys or sells offi cial reserves (dollars) and, at the same time, issues or retires a

corresponding quantity of its own bonds (which we will refer to as sterilization bonds). While

highly stylized, this assumption is the same as in the recent papers of Benes et al. and Vargas

et al. It also corresponds closely to actual practice in some countries. For example, Vargas et

al. explain the Colombian experience en some detail, and how the practice of FX intervention

led Colombia’s government to issue sterilization bonds. The same specification is incorporated

in modern textbooks, e.g. Feenstra and Taylor (2014).

In our model, it will become apparent, FX intervention can affect equilibria because the

matching sterilizing operation may relax or tighten the external credit constraint. This ar-

gument was stressed in Céspedes, Chang, and Velasco (2017) and differs from older ones, in

particular with the traditional portfolio balance view. That view relied on the assumption that

sterilization operations involved securities denominated in domestic currency, so that FX inter-

vention must change the ratio of foreign currency assets to domestic currency assets in private

hands. If, in addition, securities denominated in different currencies were imperfect substitutes,

10

restoring equilibrium would require a change in relative rates of return. Such an argument is

obviously inapplicable in our model, as we have assumed that all securities are denominated in

dollars and are perfect substitutes. But this is only to emphasize that the mechanism by which

FX intervention works is not a portfolio balance one.

It should be noted that we assume that sterilization bonds are held by domestic agents,

banks in this case. This assumption is natural and realistic, and no different from what is

usually imposed in the literature. But it is a crucial part of our argument. If the central bank

could freely sell sterilization bonds to the rest of the world, then the economy as a whole would

effectively face no external collateral constraint. Under our assumptions here, it is key that

sterilization bonds add to the economy’s overall debt, which has a limit. One can presumably

adapt our analysis to alternative scenarios as long as they imply that sterilization bonds interact

with financial frictions (in fact, this is the case of Benes et al. and Vargas et al.).

As mentioned, central bank bonds are assumed to yield the same interest rate as private

loans, %t. Reserves, on the other hand, are assumed to be invested abroad, at the external

interest rate R∗t . In this setup, the central bank can make operational losses (the so-called

quasifiscal deficit) if 1 + %t > R∗t . For the time being we assume that such losses, if any, are

financed via a lump sum tax on households; one implication is that the net worth of the central

bank will be constant, and normalized here to zero for convenience. These assumptions are

prevalent in the literature and necessary to proceed further. Having said this, I also stress

that they are not trivial either for the theory or in practice. Here further research is clearly

warranted; I offer further thoughts on this issue in the closing section.

Our maintained assumptions now ensure that, if ft denotes the central bank’s international

reserves, the central bank’s balance sheet is simply given by ft = bt, and that the central bank’s

quasifiscal deficit in period t is given by

Tt = (1 + %t−1 −R∗t−1)bt−1

11

Hence there is a tight link between foreign exchange intervention and the amount of central

bank bonds: selling foreign exchange reserves is a fall in ft, which then amounts to a reduction

in bt; reserves accumulation is an increase in bt.

Finally, it seems natural to assume that the central bank cannot issue international currency.

In this setting, this requires imposing that offi cial central bank reserves have a lower bound,

which we assume to be zero: ft = bt ≥ 0.

2.4 Households

The economy has a representative household with preferences that depend on consumption and

labor effort, and given by the expected value of∑∞

t=0 βtU(ct, nt), with

U(c, n) =c1−σ

1− σ −η

1 + φn1+φ

where σ and φ positive parameters.4

In each period t, the household decides how much to consume and to work, how much to

borrow from domestic banks, and much much equity to send to the banks. The period’s budget

constraint, expressed in dollars, is:

e−αt ct + kt − lt = (1 + ωt−1)R∗t−1kt−1 − (1 + %t−1)lt−1 + e−αt wtnt + vt + zt − Tt,

where wt = Wt/Pt is the real wage, vt denotes (dollar) profits from domestic firms and banks,

and Tt denotes to the lump sum taxes needed to finance the central bank’s quasifiscal deficit.

Finally, zt is an exogenous endowment of foreign goods (dollars), which can be thought of as

income earned from the ownership of a natural resource, as oil or commodities.

Finally, we follow Chang and Velasco (2017) in assuming that there is an exogenous limit,

4And as usual, if σ = 1, u(c) = log(c).

12

referred to as the domestic equity constraint, to how much bank equity the household can hold:

kt ≤ k

with k > 0 is some constant. The equity constraint reflects, presumably, some domestic distor-

tions that we do not model here.

The household’s optimal plan is straightforward. Optimal labor supply is given by

wtc−σt = ηnφt (4)

Assuming that the household borrows a positive amount, which will be the case in equilib-

rium, the usual Euler condition must hold:

c−σt = βEtc−σt+1Rt+1

where we have defined the consumption interest rate by

Rt+1 = (1 + %t)

(et+1

et

)α

Finally, the equity constraint binds in period t if and only if the return on equity, (1+ωt)R∗t ,

exceeds the cost of domestic loans, 1 + %t. As the reader can check, in equilibrium this will be

case if and only if 1+%t > R∗t . But this means that the equity constraint and the bank’s external

debt constraint must bind under exactly the same circumstances. This simplifies the analysis

considerably, since it allows us to impose, without loss of generality, that kt = k always, and

that the constraint dt ≤ θkt = θk binds if 1 + %t > R∗t and is slack if 1 + %t = R∗t .

13

2.5 Equilibrium

We assume that parameter values are such that financial frictions do not bind in the non

stochastic steady state. As is well known, in order to be able to apply approximation techniques

around that steady state, we need to make some assumption to ensure stationarity (Schmitt

Grohe and Uribe 2017). Here we assume that the external rate of return, R∗t , is given by a

world interest rate, denoted by R∗ and taken as exogenous and constant (for simplicity), plus

a spread term that depends on the amount of bank credit lt = kt + dt − bt :

R∗t = R∗ + Ψ(elt−l − 1)

= R∗ + Ψ(edt−bt−(d−b) − 1)

where l, d and b are the steady state values of domestic loans, external, debt and reserves,

respectively, and Ψ is an elasticity coeffi cient.

Two brief comments on the above specification are warranted. First, that the R∗t − R∗

spread increases with domestic loans implies that it increases with the economy’s external debt

net of reserves. This seems defensible: in fact, the (negative of the) quantity dt−bt corresponds

to measures of international liquidity emphasized in Chang and Velasco (2000) and elsewhere.

Second, we will assume that l is given exogenously. This differs somewhat from the literature,

which usually imposes an exogenous d. This is because we want to examine FX intervention

policies involving the management of reserves and central bank debt, with implications for the

steady state value of reserves b. It will become apparent that the assumption of an exogenously

given l is more transparent than an exogenous d for our analysis. Since this part of the model

is only important for technical reasons, we stick with exogenous l.

Under flexible prices, one can combine the optimal markup rule (2) and the labor supply

condition (4) to arrive at the equilibrium aggregate supply condition:

e−(1−α)t c−σt = (1− 1

ε)ηyφt /A

1+φ

14

In turn, the external resource constraint can be written as

(1− α)e−αt ct − [zt + κeχ−1t ] = dt − bt −R∗t (dt−1 − bt−1)

which says that the trade deficit in period t must be financed by increasing external debt or

reducing central bank debt, i.e., selling international reserves. As emphasized by Chang and

Velasco (2017), this constraint is a key aspect of the model, given that the collateral constraints

require

dt = θk if 1 + %t > R∗t

≤ θk if 1 + %t = R∗t

Note that the RHS of the external resource constraint can be expressed as

(dt − dt−1) + ∆t − r∗t (dt−1 − bt−1)

where we have defined r∗t = R∗t − 1 and ∆t = −(bt − bt−1) = ft−1 − ft is the size of foreign

exchange sales of the central bank in period t. This emphasizes that sales or purchases of

foreign exchange are just given changes in offi cial reserves and sterilization bonds. Also, if

reserves cannot be negative, ∆t ≤ bt−1, that is, foreign exchange operations in each period are

limited by the inherited level of reserves.

Equilibrium is now pinned down once we specify a rule for the evolution of bt, that is, a

foreign exchange intervention policy. We now turn to the analysis and implications of alternative

policies.

15

3 Reserves Accumulation and Intervention

3.1 General Considerations

As in Céspedes, Chang, and Velasco (2017), FX intervention in this model is irrelevant unless it

occurs at times of binding collateral constraints (or make financial frictions bind if they would

have not). For a more precise statement, fix any equilibrium, which we will denote with carets.

It can be checked that all of the equilibrium conditions, except the collateral constraints, can

be expressed in terms of a vector of variables that excludes dt and bt. In turn, the collateral

constraints can be rewritten as:

lt = (1 + θ)k − bt if 1 + %t > R∗t

lt ≤ (1 + θ)k − bt if 1 + %t = R∗t

Finally, the bank’s balance sheet requires:

dt = bt + lt − k

Consider any FX policy that implies an alternative process {b′0, b′1, ...} for offi cial reserves

that coincides with {b0, b1, ...} at all times except at some given date t. If the collateral constraint

did not bind at t in the original equilibrium, and does not bind under the new policy (i.e.

lt ≤ (1 + θ)k − b′t), then the policy does not affect equilibrium. The only adjustment is that

external debt adjusts to offset the change in reserves (that is, d′t = b′t + lt − k). Conversely,

to affect equilibria, a change in FX intervention policy must imply a change in bt at some t in

which either the collateral constrant binds or a nonbinding constraint becomes binding under

the new policy.

It also becomes apparent that, when collateral constraints bind, the central bank can stim-

ulate the economy by selling foreign exchange. By doing so, it redeems central bank bonds,

making room for domestic banks to increase credit to households. In this sense, and as emphas-

16

ized by Céspedes, Chang, and Velasco (2017), sterilized foreign exchange intervention "works"

because sterilization relaxes the external collateral constraint.

The way FX intervention works in this model is similar to that in Benes et al. and Vargas

et al. As in those papers, FX intervention changes the amount of sterilization bonds that

domestic banks must hold. Importantly, however, both Benes et al. and Vargas et al. impose a

financial transaction technology that implies that an increase, say, in the supply of sterilization

bonds must induce domestic banks to also increase the supply of loans to households, resulting

in a fall in the interest cost of domestic loans. As a consequence, as noted by Vargas et al.,

central bank FX purchases must always be expansionary in their model. In the model here,

in contrast, central bank FX purchases either leave the supply of loans unchanged (if financial

constraints do not bind) or increase it (if they do). And, crucially, the circumstances under

which FX purchases stimulate domestic credit are exactly those in which the economy is credit

constrained.

The alert reader might recognize that the propositions just stated extend those in Backus and

Kehoe (1989). For a large class of models, Backus and Kehoe identified conditions under which

sterilized intervention would not affect equilibria. But they also allowed for the possibility that

sterilized intervention might not be irrelevant if those conditions were not met. Our analysis

proceeds further, by asking what are the implications of intervention when they can matter.5

Intuitively, the economy will benefit if the central bank sells foreign exchange reserves when

financial constraints bind. This provides a rationale for the accumulation of offi cial reserves, if

(as we have assumed) foreign exchange reserves cannot be negative. In other words, our analysis

of FX intervention has implications for the discussion of observed reserves accumulation in

emerging economies and elsewhere.

One implication, in fact, relates to the costs of accumulating reserves. Why would the

central bank not accumulate a very large amount of foreign exchange in normal times, so as to

5In contrast, Backus and Kehoe stopped the analysis after stating that, when FX intervention can matter,its real effects depend on accompanying assumptions about fiscal policy. Here we make progress by makingspecific assumptions on the quasi fiscal deficit.

17

be ready to act if financial constraints suddenly bind? Our model highlights two aspects of the

answer. The first one is that, to finance the accumulation of reserves, the central bank borrows

from domestic banks, with an interest cost that adds to the quasifiscal deficit. In our model,

however, in normal times (i.e. when financial constraints do not bind), the interest cost is fully

offset by the interest earned on reserves. There is a second, more significant cost: central bank

reserves accumulation induces domestic banks to increase their own external debt and, hence,

place themselves closer to their foreign credit limit. This means that the economy becomes

more likely that, in response to exogenous shocks, that limit becomes binding.

In short, our model features a key tradeoff in reserves accumulation. Larger offi cial FX

reserves are necessary for the central bank to be ready to stimulate the economy at times of

binding financial constraints; but the financing of those reserves induces domestic banks to

increase international borrowing, making the economy less resilient.

3.2 Numerical Illustrations

We illustrate the main ideas in a calibrated version of the model. From the outset I stress

that the objective of this subsection is to expand and clarify our discussion, rather than em-

pirical realism. Hence we choose some of our parameter values just because of simplicity and

convenience.

A period is a quarter. In steady state, the world interest rate is four percent per year.

The steady state values of y, e, and c are all one, and the trade surplus to GDP ratio is one

percent. In the absence of foreign exchange intervention, these choices require that a steady

state debt to (annual) GDP ratio of twenty five percent, which accords well with usual values

in the literature (see e.g. Schmitt Grohe-Uribe 2017).

The final important aspect of the calibration is the debt limit θk. For purposes of our

discussion here I set it at a very stringent value, so that in steady state the economy is not

financially constrained, but close to being so. This is because my purpose is to illustrate the

workings of the model, with emphasis on the role of financial constraints.

18

Having calibrated the model, finding numerical solutions requires some nontrivial approx-

imation procedures. For the experiments reported here, I solved the model via the remarkably

useful occbin code due to Guerrieri and Iacovello (2015). occbin adapts the popular dynare

package to approximate our model regarded as having different regimes, given by times of

binding and nonbinding constraints. In response to exogenous shocks, the transition between

regimes is endogenous and part of the computation. See Guerrieri and Iacovello (2015) for

details, as well as commentary on the accuracy of the resulting approximations.

To obtain a feel for the model in the absence of foreign exchange intervention. Figure 1

displays impulse responses to a purely temporary fall in endowment income z. The broken

green lines give the responses if there were no financial constraints. In that case, as clear from

the figure, a purely temporary fall in z would be accommodated primarily by borrowing from

the rest of the world. This would allow the economy to spread the cost over time, smoothing

the response of consumption. The exchange rate would depreciate, but only by a small amount.

Finally, the interest rate on loans (%) would essentially remain the same (it increases minim-

ally only because the increase in the debt raises the spread R∗t − R∗ through the debt elastic

mechanism, which is negligible).

With occasionally binding financial constraints, the impulse responses are given by solid

blue lines. External debt increases to the credit limit, which binds for thirteen periods. The

binding constraint implies that, in response to the fall in z, consumption contracts substantially

more than without the constraint. As households would like to borrow more, the real interest

rate of domestic loans increases substantially. For this to happen, there is both a large increase

in the loan interest rate and a large real depreciation.

Hence the model implies that binding financial constraints can exacerbate the real impact

of adverse external shocks. It bears mentioning that the assumption in Figure 1 is that the

fall in z is large enough that the debt constraint becomes binding. If it does not, the impulse

responses just coincide with the ones without financial constraints (in the figure, the solid and

dashed lines coincide if the fall in z is small enough).

19

0 5 10 15 20 25 30 35 402

2.5

3

3.5

4

4.5

5x  10­3 Ex ternal Debt

0 5 10 15 20 25 30 35 40­1.4

­1.2

­1

­0.8

­0.6

­0.4

­0.2

0x  10­3 Cons umption

0 5 10 15 20 25 30 35 400

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6x  10­3 Ex change Rate

0 5 10 15 20 25 30 35 40­2

­1

0

1

2

3

4

5

6

7

8x  10­4 Interes t Rate on Loans

Figure 1: Responses to a Fall in z

20

0 200 400 600 800 1000­0 .015

­0 .01

­0 .005

0

0.005

0.01

0.015

0.02Ex ternal D ebt

0 200 400 600 800 1000­6

­4

­2

0

2

4

6x  10­3 C ons umption

0 200 400 600 800 1000­6

­4

­2

0

2

4

6

8x  10­3 R eal Ex c hange R ate

0 200 400 600 800 1000­7

­6

­5

­4

­3

­2

­1

0

1

2

3x  10­3 Interes t R ate on Loans

Figure 2: A Simulation

Figure 2 shows the first one thousand periods of a typical simulation. The figure illustrates

two aspects of the calibration. First, the value of the debt limit, given by θk, combines with the

stochastic process for exogenous shocks to give the frequency with which financial constraints

bind. For the figure, I assume i.i.d. shocks with standard deviation of one percent. Then θk

is set so that the collateral constraint binds about one fourth of the time. This may be too

frequent for realism, but again our purpose here is to illustrate the workings of the model.

Second, the figure emphasizes that times of binding constraints are also times of high volat-

ility in consumption, the real exchange rate, and interest spreads.

We turn to the impact of intervention policy. To start, let us assume that intervention is

given by the simple autorregresive process:

bt = Max{0, (1− ρb)b+ ρbbt−1 + εbt}

21

where εbt is an iid process, which could be interpreted as an unanticipated central bank purchase

of reserves. Here, b is the steady state stock of reserves. For ease of exposition, we assume that

0 < b < (1 + θ)k − l, that is, we assume a policy such that foreign reserves are strictly positive

and the external constraint does not bind in the steady state.

Under the above assumption on b, and intuitively, small FX operations (i.e. values of εbt

of small absolute value) do not affect real equilibria, and there are matched one for one by

changes in dt. The impact of large εbt is asymmetric. A large negative εbt prescribes a large

sale of offi cial reserves. But reserves are bounded below by zero, so the central bank runs out

of reserves. This is the only important impact in the model, however: the fall of reserves is

completely offset by a decrease in external debt, leaving domestic credit untouched.

In contrast, a suffi ciently large unanticipated purchase of reserves brings the economy to the

financially constrained region. Figure 3 depicts such a possibility. As in the previous figures,

the dashed green lines depict impulse responses to a positive εbt in the absence of financial

constraints. In this case, as shown in the figure, the accumulation of reserves would be exactly

matched by an increase in the external debt of the banks, with no other real effect. In contrast,

the solid blue lines are the responses taking into account financial constraints. The central

bank intervention requires an increase in the amount of stabilization bonds, leading domestic

banks to borrow abroad up to the credit limit. In this case, the economy remains financially

constrained for two periods. Because of the credit limit, loans to domestic households must

fall, which explain the fall in consumption, the increase in the loan interest rate, and the real

exchange rate depreciation. Finally, the real depreciation is responsible for the output increase

on impact. In short, the large purchase of FX reserves leads to the exhaustion of external credit

and a domestic credit crunch.

This discussion illustrates the main tradeoff associated with the average level of reserves

b. A low b raises the possibility that the central bank runs out of reserves. A high b, on the

other hand, requires external credit and uses up some of the country’s credit limit, making the

economy more likely to fall into the financially constrained region in response to exogenous

22

0 5 10 15 20 250

0.002

0.004

0.006

0.008

0.01FX Reserves

0 5 10 15 20 25­2

0

2

4

6

8

10x  10­3 Ex ternal Debt

0 5 10 15 20 25­0.01

­0.005

0

0.005

0.01Cons umption

0 5 10 15 20 25­0.02

­0.01

0

0.01

0.02

0.03Interes t Rate on Loans

0 5 10 15 20 25­0.01

­0.005

0

0.005

0.01

0.015Ex change Rate

0 5 10 15 20 25­4

­2

0

2

4x  10

­3 Output

Figure 3: An Excessive Purchase of Reserves

23

0 5 10 15 20 25­2

­1

0

1

2

3

4x 10­3

Figure 4: Vulnerability and the Level of Reserves

shocks.6

To illustrate further, Figure 4 shows how the response of external debt to an unanticipated

purchase of reserves depends on the average value of reserves b. The dashed line corresponds

to a lower average level of reserves (a lower value of b) than the solid line. In each case, the

figure shows the response of debt relative to its steady state value, which depends on b (since

d = l − b). The purchase of reserves is of the same magnitude and results in the external

constraint binding in both cases. However, as shown, with lower b, external debt can expand

by more before hitting the credit limit. In addition, the economy exits the constrained region

faster than with higher b.

The above considerations shed light on the implications of intervention rules that respond

to endogenous variables, such as exchange rates. Consider, for instance, an intervention rule of

the form:

bt = Max{0, (1− ρb)b+ ρbbt−1 − υe(et − e)} (5)

6This argument is reminiscent of that of Alfaro and Kanczuk (2006) in the context of sovereign debt. Intheir model, increased offi cial reserve levels may reduce the amount of sovereign debt that is sustainable. Themechanisms in that paper, however, are quite different to ours, and they do not bear on the issue of FXintervention.

24

where υe ≥ 0. According to this rule, the central bank buys foreign exchange when the exchange

rate is stronger than its steady state value, and sells it when the exchange rate is abnormally

weak, with the size of the response given by the coeffi cient υe.

It should be clear how the policy may help stabilization in the face of shocks that make

financial constraints bind. In that case, the central bank sells reserves in response to the real

depreciation. The resulting fall in the quantity of stabilization bonds frees domestic banks to

extend additional credit to households, who want it in order to smooth consumption. This is

depicted in Figure 5. In the figure, the dashed green lines are impulse responses to a fall in z

assuming that υe = 0, that is, that FX intervention does not respond to the exchange rate. In

that case, there is no FX intervention at all. The shock is assumed to be large enough that the

economy hits the credit constraint. Domestic credit increases, but not enough to satisfy the

increased demand for credit. Consumption then falls, the exchange rate depreciates, and the

interest rate on loans goes up.

The solid blue lines assume that υe > 0. Since the fall in z leads to depreciation, the central

bank sells reserves. As it does so, it retires stabilization bonds, freeing resources for domestic

banks to increase loans to households. As a result, the fall in consumption is less acute, and

the adjustments in the real exchange rate and interest rates less sharp.

While an FX intervention rule of the form is beneficial in stimulating the economy when

financial constraints become binding, it also has pitfalls. In particular, it prescribes that there

is intervention in response to exchange rate movements even when financial constraints do not

bind, which is at best ineffective and, at worst, can be detrimental.

To see this, suppose that financial constraints do not bind, and the economy is hit by an

unanticipated increase to z. This should be beneficial: the economy can afford more consump-

tion, and the exchange rate tends to appreciate. The intervention rule then prescribes that the

central bank will accumulate reserves. If the accumulation of reserves is small, because either

the shock is small enough or the elasticity υe is small, then the economy remains financially

unconstrained. But if the increase in reserves is large enough, the financial constraint will bind.

25

0 5 10 15 20 25­2

­1 .5

­1

­0 .5

0x  10­3 FX R es erv es

5 10 15 200

0.5

1

1.5

2

2.5

3

3.5

x  10­3 D omes tic  C redit

0 5 10 15 20 25­0 .01

­0 .008

­0 .006

­0 .004

­0 .002

0C ons umption

0 5 10 15 20 250

0.005

0.01

0.015

0.02Interes t R ate on Loans

0 5 10 15 20 250

0.005

0.01

0.015Ex c hange R ate

0 5 10 15 20 250

1

2

3

4

5x  10­3 Output

Figure 5: Exchange Rate Based FX Intervention

26

In order to accommodate the sterilization bonds of the central bank, domestic banks must then

reduce loans to households. In other words, the financing of FX intervention can crowd private

credit out.

This is depicted in Figure 6. As before, dashed lines are impulse responses when there are

no financial constraints. An unanticipated increase in z induces the representative household

to consume more and, at the same time, to borrow less. The exchange rate appreciates, as

expected. In response, the central bank buys foreign exchange; the increase in the quantity of

sterilization bonds more than compensates for the fall in the private demand for credit, and

external debt increases. In the absence of financial constraints, increased external borrowing

does not affect the cost of domestic loans.

In our model, however, the FX intervention rule implies that the economy hits the external

constraint, which remains binding for a number of periods. To accommodate the increase in

central bank sterilization bonds, domestic credit falls by more than in the absence of financial

constraints. This means that domestic consumption must fall, which is associated with an

increase in the interest rate on domestic loans. Note that the exchange rate appreciates by

less than in the unconstrained case. Hence the FX intervention policy looks like it succeeds at

stabilizing the exchange rate. But, as it becomes evident, this is the case only because it also

creates a credit crunch.

The disadvantage of a FX intervention rule that responds to the exchange rate is, therefore,

that it prescribes intervention even it is not justified by binding financial constraints. This

suggests that there is a superior strategy: intervention should occur if interest rate spreads

widen, as in:

bt = Max{0, (1− ρb)b+ ρbbt−1 − υ%(1 + %t −R∗t )} (6)

with υ% ≥ 0 giving the elasticity of central bank sales to widening spreads. This rule implies that

the central bank sells foreign exchange, relaxing financial constraints, when the loan interest

rate increases above the cost of international credit (which signals that financial constraints

27

0 5 10 15 20­0 .1

0

0.1

0.2

0.3FX R es erv es

0 5 10 15 20­0 .1

­0 .05

0

0.05

0.1

0.15Ex ternal D ebt

0 5 10 15 201.5

2

2.5

3

3.5

4x  10­3 C ons umption

0 5 10 15 20­5

0

5

10

15x  10­4 Interes t R ate on Loans

0 5 10 15 20­4 .5

­4

­3 .5

­3

­2 .5

­2

­1 .5x  10­3 Ex c hange R ate

0 5 10 15 20­0 .1

­0 .09

­0 .08

­0 .07

­0 .06C red it

Figure 6: Pitfalls of Exchange Rate Based FX Intervention

28

bind). When financial constraints do not bind, however, the spread is zero in our model, so

that no intervention is called for (over and above what is required to bring the level of reserves

back to its steady state value b).

Responses under this rule to a fall in z are given in Figure 7. The fall in z raises the

households’demand for credit, which banks try to accommodate by borrowing abroad. As the

credit limit is hit, the spread of the domestic loan rate over the foreign interest rate widens.

The intervention rule then implies that the central bank sells reserves, reducing bt and allowing

domestic credit to expand further. This helps stabilizing credit spreads, consumption, output,

and the exchange rate.

The shape of the responses in Figure 7 is similar to the ones in Figure 6, and the intuition

is also very close, the main difference being the variable to which FX intervention reacts to

(the exchange rate in Figure 6, credit spreads in Figure 7). But this difference is crucial when

financial constraints do not bind, in which case there is active FX intervention with the exchange

rate-based policy, but none with the spreads-based policy.

29

0 5 1 0 1 5 2 0 2 5­ 1 0

­ 5

0

5x   1 0

­4 F X   R e s e r v e s

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 40

1

2

x   1 0­3 D o m e s t ic   C r e d it

0 5 1 0 1 5 2 0 2 5­ 4

­ 3

­ 2

­ 1

0x   1 0

­3 C o n s u m p t io n

0 5 1 0 1 5 2 0 2 5­ 5

0

5

1 0x   1 0

­3 I n t e re s t   R a t e   o n   L o a n s

0 5 1 0 1 5 2 0 2 50

2

4

6x   1 0

­3 E x c h a n g e   R a t e

0 5 1 0 1 5 2 0 2 50

0 . 5

1

1 . 5

2x   1 0

­3 O u t p u t

Figure 7: Intervention to Stabilize Credit Spreads

4 Nominal Rigidities and Monetary Policy

To allow for the study of conventional monetary policy, we now drop the assumption that

domestic producers adjust nominal prices every period. Following the recent literature and

adopt the well known Calvo protocol. Because this specification is well known, we only give a

brief description here, and refer interested readers to Gali (2015) for details.

In any given period, an individual producer can set a new price for her product only with

some probability (1 − θ) < 1. Because producers cannot set prices every period, they do not

set the static optimal markup when they can, and equation (2) is dropped. Instead, producers

able to change prices choose them so that the markup over marginal cost that is optimal, on

average, for the random period of time until they can change prices again. As shown in Gali

(2015), to a first order approximation, domestic inflation, denoted by πht = logPht − logPht−1,

is determined by

πht = βEtπh,t+1 + λ(logmct − µ) (7)

30

where mct = MCt/Pht denotes marginal cost in terms of domestic goods, µ = log(1− 1ε) is its

steady state value (in logs), and the coeffi cient λ is given by

λ =(1− θ)θ

(1− βθ)

Domestic inflation now depends on current and future real marginal costs. In turn, marginal

costs in our model are determined by technology, as given by (1), and optimal labor supply (4).

These conditions imply:

mct =MCtPht

=(Wt/At)

Pht(8)

= ηe1−αt cσt y

φt /A

1+φ

Solving the model now requires one more equation, which is given by a monetary policy rule.

Our model is cashless but, as discussed by Woodford (2003), this is not an issue if monetary

policy is given by an appropriate interest rate rule of the Taylor type. As advocated by Romer

(2000), here we assume that the central bank sets policy in order to steer the expected real

interest rate:

it ≡ EtRt+1 = Et(1 + %t)

(et+1

et

)αThen we posit a Taylor rule such as:

it = logR∗t + φππt + umt (9)

To get a sense of the implications, Figure 8 displays impulse responses to a contractionary

monetary shock (positive umt) that is large enough to place the economy in the financially

constrained region. The dashed green lines assume no financial constraints, while the solid

blue lines take binding constraints into account. The shock directly raises the expected con-

sumption based interest rate (by assumption), and therefore consumption growth. In response,

31

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2Monetary Shock

0 2 4 6 8 10 12 14 16 18 200

0.02

0.04Policy Rate

0 2 4 6 8 10 12 14 16 18 20­0.04

­0.02

0Consumption

0 2 4 6 8 10 12 14 16 18 200

0.01

0.02

External Debt

0 2 4 6 8 10 12 14 16 18 200

0.005

0.01

0.015Interest Rate on Loans

0 2 4 6 8 10 12 14 16 18 20­0.2

0

0.2Exchange Rate

0 2 4 6 8 10 12 14 16 18 20­0.1

0

0.1Output

0 2 4 6 8 10 12 14 16 18 20­0.06

­0.04

­0.02

0Domestic Inflation

Figure 8: A Contractionary Monetary Policy Shock

consumption must fall on impact.7 Households attempt to cushion the blow by borrowing from

domestic banks, so domestic loans increase. But this mechanism is limited if there are financial

constraints. As the figure shows, the limit on external credit is reached on impact: if there

had been no constraints (dashed lines), consumption would fall less and external debt would

increase more than in the presence of constraints (solid lines). To ration credit in the case of

binding constraints, the interest rate on domestic loans, 1 + %t, rises above and over the world

interest rate.

Importantly, the exchange rate appreciates in response to this kind of shock, but binding

financial constraints limit the extent of the appreciation. This means that domestic inflation

and output fall by less and that the policy rate increases than more than in the absence of

financial constraints.

This exercise emphasizes that not only monetary policy is powerful in this model, but also

that binding financial constraints can exacerbate the real impact of monetary shocks.

We might now ask about the role of FX intervention. Our first observation is that, as in

7NB For this experiment I assumed that the CRRA is 2. Under log utility, there is no impact on the levelof debt.

32

the model with flexible prices, FX intervention cannot have real effects if it occurs at times

of nonbinding constraints. The argument is virtually the same as in subsection 3.1, except

that the relevant system of equilibrium equations excludes (2) and includes (7), (8), and (9),

and the intuition is unaltered: if the collateral constraint does not bind at t, any change in bt

(which leaves the constraint still not binding) is offset one for one by a change in dt, without

any impact on equilibrium.

A notable implication is that, independently of monetary policy, FX intervention policy does

not impact real allocations for small enough shocks, that is, shocks that do not make financial

constraints bind. This is clear under intervention rules such as (5) or (6). In fact, if FX

intervention is triggered by abnormally high credit spreads, as in (6), there is no intervention at

all as long as constraints do not bind. If FX intervention responds to the exchange rate, shocks

that do not imply binding financial constraints do trigger sales or purchases of reserves, but ones

that are fully accommodated by changes in external debt dt, with no impact on equilibrium.

For large enough shocks, financial constraints bind and, as we have stressed, FX intervention

can have real effects, and can complement conventional monetary policy. To illustrate, Figure

9 displays responses to a fall in z, assuming a Taylor rule like (9), and either no active FX

intervention (dashed green lines) or FX intervention that responds to spreads (solid blue).

Without an active FX intervention response, the shock would raise the domestic demand for

private loans. Banks would then borrow abroad up to the credit limit, and the loan interest rate

would increase to ration credit. The exchange rate would depreciate, leading to an increase in

the foreign demand for domestic output, which explains the output increase. As a consequence,

domestic inflation increases. Then the Taylor rule prescribes an increase in the policy interest

rate.

With an FX rule as (6), the increase in spreads prompts the central bank to sell reserves.

As discussed, the corresponding fall in sterilization bonds allows for domestic loans to increase

by more than in the absence of FX intervention. For this calibration, the FX rule has negligible

effects on the impact response of consumption, although it implies a smoother transition back

33

0 5 10 15 20­2

­1

0

1x  10­3 R es erv es

0 5 10 15 20­5

0

5

10x  10­3 Polic y  R ate

0 5 10 15 20­6

­4

­2

0x  10­3 C ons umption

2 4 6 8 10 12 14 16 18 200

1

2

3

x  10­3 D omes tic  C redit

0 5 10 15 20­0 .01

0

0.01

0.02

0.03Interes t R ate on Loans

0 5 10 15 200

0.01

0.02

0.03Ex c hange R ate

0 5 10 15 200

0.005

0.01

0.015

0.02Output

0 5 10 15 20­2

0

2

4

6x  10­3 D omes tic  Infla tion

Figure 9: FX Intervention and Monetary Policy

to the steady state. More notably, the active FX rule moderates the exchange rate depreciation,

and hence the increases in output and domestic inflation.

This analysis reveals that, in the presence of financial frictions, the question of whether

sterilized FX intervention can be an independent policy instrument has an unambiguously

positive answer. But the answer differs substantially from others offered in the recent literature.

Sterilized FX intervention is ineffective locally: it cannot benefit for shocks small enough that

financial constraints do not bind. Intervention can help when the constraints bind, and in that

case it works by alleviating the external credit limit.

On the other hand, nonlinearities are essential. Hence proper analysis of FX intervention

requires going beyond currently fashionable approaches that restrict attention to local approx-

imate behavior around the steady state.

34

5 The Role of Financial Dollarization

Our models so far have study an economy that is "financially dollarized", in which all financial

instruments are denominated in dollars. This was partly because some actual economies are

financially dollarized, and partly because we wanted to emphasize that the arguments presented

here do not depend on currency mismatches or debt denomination.

In many economies, however, some securities are denominated in pesos along with others

that are dollar denominated. In this section we argue that, while some additional effects are

introduced in the model through that alternative assumption, our line of reasoning remains

largely untouched.

We assume now that domestic loans and central bank bonds are denominated in pesos,

paying a gross interest rate Rnt between periods t and t + 1. What is crucial is that Rn

t is

determined in period t : the arguments of previous sections obviously apply if return on peso

securities are indexed to, say, the dollar. In that case, the dollar return on loans and bonds

between t and t+ 1 depends on the realized rate of depreciation, and is given by

Rdt+1 = Rn

t

EtEt+1

Observe the notation: the subscript on Rdt+1 emphasizes that it is a random variable that

becomes known only at t+ 1. This requires amending our analysis of the decision problems of

domestic agents.

To simplify things, now we assume simply that domestic banks belong to households, which

provide equity k. Then the typical bank’s problem is to maximize the discounted expected value

of dollar profits:

EtMt+1πt+1

where

πt+1 = Rdt+1(lt + bt)−R∗tdt

35

subject to bt + lt = k + dt and the collateral constraint dt ≤ θk, where Mt+1 is the household’s

discount factor for dollar payoffs, which we derive shortly.

The first order conditions to this problem imply that the collateral constraints now can be

written as:

dt = θk if EtMt+1(Rdt+1 −R∗t ) > 0

≤ θk if EtMt+1(Rdt+1 −R∗t ) = 0

Note that these conditions are very similar to the ones we derived earlier, in the case of

financial dollarization.

The analysis of the central bank is the same as before, observing only that the quasifiscal

deficit in period t is now given by

Tt = (Rdt −R∗t−1)bt−1

and hence it depends on the realized rate of depreciation.

Lastly, the household’s problem is solved just as before, but now we need to take into

account that the dollar interest rate on loans taken at t is Rdt+1 instead of 1 + %t, and hence it

is uncertain as of period t. The Euler condition for loans then becomes:

c−σt = βEtc−σt+1R

dt+1

(et+1

et

)α

or

1 = EtMt+1Rdt+1

which identifies the dollar discount factor as:

Mt+1 = β

(ct+1

ct

)−σ (et+1

et

)α

36

The expected consumption-based real rate is EtRdt+1

(et+1et

)α.With these modifications, we

can retrace the analysis above, without significant change. To illustrate, Figure 10 presents

impulse responses to a fall in z. The figure assumes a Taylor rule of the form (9), and an FX

intervention rule similar to (6) but with EtRdt+1 − R∗t as the relevant spread. In the absence

of financial constraints (dashed green lines), the shock would be accommodated by increased

household borrowing, and an increase in the banks’external debt, without noticeable impact on

real variables or inflation. Given the policy rules, the central bank does not change the policy

interest rate nor intervenes in the foreign exchange market.

The shock is assumed to be large enough for external debt to hit the credit limit, however.

As discussed before, adjustment then entails a larger fall in consumption, which requires an

increase in the real interest rate. This is accomplished via a relatively large devaluation and,

in this model, an increase in the nominal peso interest rate on loans. The monetary policy rate

increases in response to rising inflation, and reserves fall because credit spreads widen.

6 Final Remarks

This paper was advanced an alternative view of the way sterilized FX intervention works,

and derived several implications for theory and policy. As promised in the introduction, this

perspective can help reconcile theory and practice in compelling, intuitive ways.

As for the theory, I have shown that occasionally binding financial constraints imply that

sterilized FX intervention can have real effects, but only at some times, that is, if it relaxes

the financial constraints when they bind. This result is quite consistent with standard theory,

but it implies that sterilized FX intervention is not always irrelevant. And in fact, our analysis

suggests that FX intervention can be powerful when it matters the most.

Our analysis also suggests that FX intervention may be irrelevant much, or even most, of

the time. In this sense, it is no surprise that empirical evidence for significant effects of FX

intervention has been elusive. Future empirical research should examine whether the impact of

37

0 5 10 15 20­0 .06

­0 .04

­0 .02

0

0.02R es erv es

0 5 10 15 200

0.5

1

1.5

2x  10­3 Polic y  R ate

0 5 10 15 20­0 .01

­0 .008

­0 .006

­0 .004

­0 .002

0C ons umption

0 5 10 15 200

0.01

0.02

0.03

0.04

Ex ternal D ebt

0 5 10 15 200

1

2

3x  10­3 Pes o Interes t R ate on Loans

0 5 10 15 200

0.005

0.01

0.015Ex c hange R ate

0 5 10 15 200

2

4

6x  10­3 Output

0 5 10 15 20­5

0

5

10x  10­4 D omes tic  Infla tion

Figure 10: A Fall in z with peso securities

38

FX intervention depends on the incidence of financial constraints.

More generally, our analysis stresses that the impact of sterilized FX intervention may

depend on the degree of financial frictions as well as the nature of financial institutions. This

suggests that, empirically, the effectiveness of FX intervention should differ across countries,

according to their degree of financial development.

For exposition, we made very specific assumptions along several dimensions. One of them

was that the central bank used its own sterilization bonds in sterilization operations. A little

thought should convince the reader that this assumption is much less restrictive than it appears.

For instance, suppose that, for sterilizing FX purchases, the central bank sells government debt

instead of its own debt. The impact of this operation would be exactly the same as the one in

this paper, assuming that government debt has to be absorbed by domestic banks. In fact, one

profitable way to look at this alternative is to think of the "central bank" in this paper as a

consolidated entity encompassing the central bank plus the fiscal authority.

In this regard, it was mentioned that our analysis was developed under a specific assumption

on the central bank quasifiscal deficit. If that assumption were to be dropped, one would have to

supply further details about how the quasifical deficit is financed and, further, what determines

the evolution and management of the central bank’s net worth. These are not trivial issues,

but best left for future research. Let us only remark that this question is related to the more

general claim that unconventional policy may matter if there are frictions in the links between

the central bank and fiscal authorities. See, for example, Benigno and Nistico 2015).

This paper has focused on the transmission mechanism behind FX intervention, and sug-

gested some ways in which intervention may be beneficial in terms of welfare. But it has not

attempted to characterize welfare maximizing policy, which is a promising avenue for future

studies. A related question is that of optimal reserves management in our model. Our discus-

sion has stressed a novel trade-off in holding large stocks of reserves, namely that the central

bank is in a better position to deal with suddenly binding financial constraints, against the

fact that the financing of the reserves may imply that the constraints bind more often. This

39

indicates that an optimal reserves policy may have to take into account precautionary motives

of the kind stressed in the recent macroprudential policy literature. But this is a substantial

task, and hence delayed to further research.

40

AppendixHere we provide details on the calibration used for the examples and illustrations. I assume

that there is a steady state in which the external constraint does not bind. (It should be noted

that this assumes that FX intervention policy is consistent with such a steady state.)

We denote steady state values with overbars. Then, 1 + % = R∗ (which here denotes the

steady state value of both R∗t and R∗t ) because financial constraints do not bind. The Euler

condition then requires that βR∗ = 1, as usual.

The steady state values of y, c, and e must satisfy:

y = αe(1−α)c+ xeχ

(1− α)e−αc− [z + κeχ−1] = −r∗(d− b)

1/η(1− 1/ε) = e(1−α)yφcσ/A1+φ

where r∗ = R∗ − 1

For calibration, I impose that the steady value of e be one, and that the trade balance

surplus be one percent of output (it is common to impose balanced trade in the steady state,

but Schmitt Grohe and Uribe 2017 argue in favor or a surplus of two percent of GDP; as a

compromise, I impose one percent). Now, from the definition of trade surplus, this requires:

[z + κ]− (1− α)c

= z + y − c

= 0.01y

the second equality following from market clearing (y = αc+ κ)

Optimal labor supply reduces to

Θ = cσyφ/A1+φ

41

where

Θ = 1/(1− 1

ε)η

I choose parameters so that y = c = 1 as well. For the market clearing condition to be

satisfied, this will require κ = 1− α. Also, for optimal output,

A = Θ−(1/1+φ) =

((1− 1

ε)η

)1/1+φ

and

z = 0.01

Finally, for the country budget constraint to hold, we need that

0.01 = z = r∗(d− b)

This restricts (d − b). The usual assumption is that b = 0; if so, d = z/r∗. If we assume

r∗ = 0.01,then d = 1. (Note that this is the ratio of debt to quarterly output. So, it corresponds

to 0.25 in terms of the usual debt/annual GDP ratio, and so it is in the ballpark. )

42

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